Half Flip 6D Lattice R. B. Palmer, Rick Fernow (BNL) Thursday - PowerPoint PPT Presentation

Half Flip 6D Lattice R. B. Palmer, Rick Fernow (BNL) Thursday 2/14/13 • Introduction • lattice types • Parameters of Half-Flip lattices • ICOOL simulation using matrices • Conclusion 1

Cooling Scheme Advanced 4D Final Baseline 4D Final Advanced 3D Cooling 6D before merge Initial Phase Rotation • 4 6D after merge 2 Emit long (mm) 6D Merge Final 10 2 8 • ◦ 6 ◦ ◦ 4 ◦ ◦ ◦ ◦ 2 ◦ ◦ ◦ ◦ ◦ 10.0 ◦ ◦ 8 ◦ ◦ 6 ◦ ◦ ◦ 4 ◦ ◦ ◦ ◦ ◦ ◦ ◦ 2 ◦ 1.0 8 150 240 6 10 2 10 3 10 4 10.0 Emit trans (micron) 2

RFOFO Flip Bo 11.66 max Bs 15.04 11.49 maxRBJs 260.8 310.0 Brf 10.0 (cm) Axial Fields (T) 154 -154 20 ◦ ◦ ◦ 184 -184 ◦ 0 Radii -20 0 25 50 75 100 125 Length (cm) 3

Non-Flip Rick: this has no stable orbits, unless very little bending 4

Half Flip no tilt/ tilt Radii (cm) Axial Field (T) 114 114 -114 -114 -114 -114 114 114 (cm) 1.5 π / 3 π 20 2 π / 4 π 1 π / 2 π beta 4 0 2 -20 0 150 175 200 225 250 Momentum (MeV/c) 0 25 50 75 100 125 Length (cm) • Without bending all cells have identical focusing ( ∝ B 2 ) • With bending (Guggenheim), or coil tilting (Balbakov) the symmetry is broken and a resonance exists in the center of the pass band • But the coil tilts are very small and this resonance may not be too bad 5

Coil dimensions file β cell L dL R dR j A/mm 2 cm cm cm cm cm cm 70 5.2 68.75 3.000 28.000 18.000 15.000 117.26 71 4.6 68.75 0.000 29.000 18.000 15.000 105.77 72 3.9 68.75 0.000 13.000 12.000 15.000 96.80 13.000 16.000 18.000 15.000 96.85 74 2.9 58 4.218 8.436 5.905 21.091 158.14 12.655 6.327 19.404 7.593 134.22 76 2.1 58 1.687 10.967 4.218 16.873 153.79 77 1.6 58 0.000 10.967 4.218 16.873 158.75 • locations and dimensions are symmetric left-right in each cell • currents are reversed left-right in each cell • when there are two lines for one file, there are two coils per half cell 6

j vs B for required 3 cm betas RFOFO flip magenta Half flip lattices red shorter blue longer Non-flip black 60% YBCO good direction 25% NbSn 1.9 4 25% NbTi 1.9 j (a/mm 2 ) 3 ◦ ◦ • 3 ◦ ◦ • 3 ◦ 2 ◦ • 3 ◦ ◦ 3 • 50% BSCCO cable ◦ ◦ ◦ • ◦ ◦ ◦ ◦ ≈ YBCO bad direction ◦ ◦ ◦◦ 10 2 ◦ 9 ◦ ◦ ◦ 8 42 ◦ 7 6 0 10 20 30 B on coil (T) • Half flip design uses less fields on coils than Non-flip but its cells are longer • They are now ok for both Nb 3 Sn and YBCO in the bas direction • In addition, the field lines are more axial than in the flip lattice 7

j vs B extended to lower betas RFOFO flip magenta Half flip lattices red shorter blue longer Non-flip black 60% YBCO good direction 25% NbSn 1.9 4 1.8 ◦ 25% NbTi 1.9 j (a/mm 2 ) 3 ◦ ◦ • 3 ◦ ◦ ◦ • 3 ◦ ◦ ◦ ◦ 2 ◦ 1.6 ◦ ◦ • 3 1.6 ◦ 3 ◦ • ◦ ◦ 50% BSCCO cable ◦ ◦ ◦ • ◦ ◦ ◦ ◦◦◦ ≈ YBCO bad direction ◦ ◦ 10 2 ◦ 9 ◦ ◦ ◦ 8 ◦ 42 7 6 0 10 20 30 B on coil (T) • Half flip solution probably ok to 1.6 cm with longer cells • This should cool to 150 µ m for the enhanced performance goal 8

ICOOL using matrices for half-flip with longer cells 45 222324252627282930 31 70 71 72 74 76 77 10 3 freq 805 10 2 46.25 31.59 Transm % 10.0 1.98 1.91 ǫ � mm 1.0 0.24 0.15 ǫ ⊥ mm 0.1 0 200 400 600 length (m) • Performance should be a little better with shorter cells • And this has not been optimized yet 9

Conclusion ǫ ⊥ =240 µ m ǫ ⊥ =150 µ m case files Len ǫ � Trnsm. % Len ǫ � Trnsm. % 1 tap16a0 RFOFO 470 2.1 47.3 3 tap16a5v Non-flips 375 2.1 53.7 471 2.15 46.2 3 tap16a5x Half flips 410 1.98 46.2 510 1.91 31.6 • Half-Flip lattice meets current density requirements • And meets minimum cooling requirements (240 µ m) – More losses than Non-Flip – But about the same as original RFOFO Flip lattices • Even meets extended cooling requirement (150 µ m) – But with more losses than Non-Flip • But may have additional losses from resonance in center of acceptance if bending one way • Rick: Simple coil tilts did not give enough dispersion – Perhaps the Valeri Balbakov version would allow more flexibility in the generation of dispersion • Needs real simulation with/without Balbakov modification 10